On the topological side, the ambient 3-manifold is assumed for simplicity to be \(S^3\) , and there would be significant work required to extend the results to links embedded in more general 3-manifolds. We note that some authors do work in slightly greater generality, for instance, in [1]}, results are proven for rational homology 3-spheres. We come to the definition of a knot and more generally, a link. We refer to [2]} and [3]} for a comprehensive treatment of some of the basic notions in knot theory, as well as definitions that are equivalent to that given below, which we have chosen since in our estimation, it is easiest to state.
